Solve the problems. 1 Miguel is making trail mix. He uses $$ 5 \frac{1}{3} $$ ounces of nuts and $$ 2 \frac{3}{4} $$ ounces of raisins. Which of these is a reasonable estimate for how many more ounces of nuts than raisins Miguel uses?

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To solve the problem, we need to find out how many more ounces of nuts than raisins Miguel uses. We will follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Subtract the amount of raisins from the amount of nuts.
3. Estimate the result.

### Step 1: Convert Mixed Numbers to Improper Fractions

- For nuts: 
  $$
  5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3}
  $$

- For raisins:
  $$
  2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}
  $$

### Step 2: Subtract the Amount of Raisins from the Amount of Nuts

Now we need to find the difference:
$$
\text{Difference} = \frac{16}{3} - \frac{11}{4}
$$

To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.

- Convert $$\frac{16}{3}$$ to a fraction with a denominator of 12:
  $$
  \frac{16}{3} = \frac{16 \times 4}{3 \times 4} = \frac{64}{12}
  $$

- Convert $$\frac{11}{4}$$ to a fraction with a denominator of 12:
  $$
  \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
  $$

Now we can subtract:
$$
\frac{64}{12} - \frac{33}{12} = \frac{64 - 33}{12} = \frac{31}{12}
$$

### Step 3: Estimate the Result

To estimate how many more ounces of nuts than raisins Miguel uses, we can round the fractions to the nearest whole numbers:

- $$5 \frac{1}{3} \approx 5$$
- $$2 \frac{3}{4} \approx 3$$

Now, we can estimate:
$$
5 - 3 = 2
$$

### Conclusion

A reasonable estimate for how many more ounces of nuts than raisins Miguel uses is approximately $$2$$ ounces.
Miguel uses approximately 2 more ounces of nuts than raisins.

Solve the problems. 1 Miguel is making trail mix. He uses \( 5 \frac{1}{3} \) ounces of nuts and \( 2 \frac{3}{4} \) ounces of raisins. Which of these is a reasonable estimate for how many more ounces of nuts than raisins Miguel uses?

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